How can I change my node group interface to more easily edit the Group Input/Output nodes?
That's just the way node groups display in the current version of Blender. The other screen shot is from an older version of Blender.

In your node group, you can edit all the input/output settings by hitting the N key which will open the property panel on the right. Clicking on each input/output in the list will allow you to change the properties for each one there.